Blow up of solutions for a Parabolic-Elliptic Chemotaxis System with gradient dependent chemotactic coefficient

2021/11/05 by Tello, J. Ignacio · 1 citation
#35B44 #35B51 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.03358

Abstract

We consider a Parabolic-Elliptic system of PDE's with a chemotactic term in a N-dimensional unit ball describing the behavior of the density of a biological species "u" and a chemical stimulus "v". The system includes a nonlinear chemotactic coefficient depending of ``∇ v", i.e. the chemotactic term is given in the form - div (χu |∇ v|^p-2 ∇ v), for p ∈ ( (N)/(N-1),2), N gt;2 for a positive constant χ when v satisfies the poisson equation - Δv = u - (1)/(|Ω|) ∫_Ω u₀dx. We study the radially symmetric solutions under the assumption in the initial mass (1)/(|Ω|) ∫_Ω u₀dxgt;6. For χ large enough, we present conditions in the initial data, such that any regular solution of the problem blows up at finite time.

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